Question

If $\vec { a }$ , , represents adjacent edges of tetrahedron such that | $\vec { a }$ | = || = || = 2 and angle between $\vec { a }$ and is p/3, and is p/3 and $\vec { a }$ andp/3 then its volume is

• A. 4 $\sqrt { 2 }$
• B. $\sqrt { \frac { 2 } { 3 } }$
• C. $\frac { 2 \sqrt { 2 } } { \sqrt { 3 } }$
• D. $\frac { 2 \sqrt { 2 } } { 3 }$

Answer 1

Answer: (D)

$\frac { 2 \sqrt { 2 } } { 3 }$

Answer 2

Let = l ( $\vec { a }$ +) + m ( $\vec { a }$ +)

taking dot product with $\vec { a }$ , we get

2 = l [4 + 2] ̃ l = $\frac { 1 } { 3 }$

squaring 4 = l2 [4 + 4 + 4] = m2. 12

̃ m2 = $\frac { 2 } { 9 }$

̃ taking dot product with ( $\vec { a }$ × )

[ ( $\vec { a }$ × ). $\overrightarrow{c}$] = m(12)

= $\frac{\sqrt{2}}{3}$× 12 = 4$\sqrt{2}$

\ volume of tetrahedron is equal to 1/6. 4$\sqrt{2}$=$\frac{2\sqrt{2}}{3}$